True Axioms of a science like physics would allow for somereplacement; biology in terms of physics.

One of the features lacking in biology, throughout biology is theimportance of electricity and magnetism in biology. Very little if anyis ever discussed or taught in biology that the living organism is sodependent on electricity and magnetism. I think the reason for thisomission and the reason that no-one in physics was smart enough in the20th century to place the Maxwell Equations as the axiom system ofphysics, is that the Maxwell Equations are so hard to understand, evenfor the best of physicists. Their understanding of the MaxwellEquations is mostly memorization, not innate understanding. Forexample, it was said of Tesla, unlike the physicists of the 20thcentury, that someone could draw the most elaborate and complexelectrical wiring and circuits and Tesla would instinctively know ifit would work or not work and point out the errors.

So, given the case of Tesla, that we can perhaps expect only oneperson per century to be comfortable with electricity and magnetismand not some Phd rote memorization of the Maxwell Equations.

Now when you have the true axioms of a science, then there is somereplacement, substitution that can occur. For example the geometryaxioms as given by Euclid and then revised by Hilbert. Now we can dosome replacement such as a plane instead of a line in the axiomsystem. For that we can still retain many of the truths such as twononparallel lines intersect in a point, whereas two nonparallelplanes intersect in a line. Or another example is that line A parallelto B, and B parallel to C is that A is parallel to C can be replacedwith Plane A, B, C where plane A is parallel to C.

The point I am making is that a true axiom system of a science subjectallows for replacement or substitution of the terms of the system,terms more complex than the original system. Now some truths of linescannot be generated from planes simply because of the increaseddimension.

But let me now transfer that understanding over to the MaxwellEquations as axioms over all of physics to that of Maxwell Equationswith substituted biology.

So in the case of physics of Faraday law we have a nucleus of an atomas a capacitor, a proton as a capacitor of stored energy of magneticmonopoles and a electron traveling around the proton capacitoras a closed loop of wire with moving electric charge in the closedloop of wire.

In biology we have a living cell and a nuclear region of DNA. DNA is acapacitor of stored information, stored energy and going around thenucleus is messenger RNA.

Alright, I do not know how far I want to dive in and elaborate on thisanalogy. What I do want to do is to refer to the fact that the truephysics axioms must be so that its terms and equations can be steppedup in complexity and thus give us other sciences. In fact, my pursuitof the geometry of the nucleus and proton and electron should beguided by biology more than I have so far done.

And, the true axioms also will reveal how very much complex theMaxwell Equations are, even though we do not step up in complexity.Here I am speaking of the concept of duality, in that our human mindsare not able to go below duality, what some have called the principleof Uncertainty, but which is really the principle of duality. TheMaxwell Equations derives the principle of Duality and the Uncertaintyprinciple.

But let me tell it so that science illiterates can even understand it.The entire observable Universe that we see is just a single electronof a single plutonium atom. So the stars, galaxies, planets and lifeare fragments, bits and pieces of one electron. Yet in the MaxwellEquations we view an electron as a tiny object of rest-mass 0.51 MeVwith a negative charge, yet that single electron is the entireobservable Universe of stars and galaxies and planets.

But, an axiom system can do that, because a plane is far more complexthan a line and we can replace a line in the axioms of geometry withplanes, to some extant. In physics, we can talk about the electron andproton as what the Faraday law is all about, but we can also talkabout the Faraday law as if it was the axiom of biology where the DNAinstructs the messenger RNA to commit some biological metabolism.

But if you examine physics with biology, you begin to realize that thevery same axiom system that delivers all of physics, when you step upthe complexity of terms, that same system that gives all of physics,gives all of biology.

What the principle of duality or Uncertainty enter the picture, isthat the terms of physics cannot go lower in meaning than what theyalready are. If the Maxwell Equations tell us that the proton is aparallel plate capacitor storing magnetic monopoles, then I cannot goany lower in meaning, but that the proton is so very complex, far morecomplex than our human mind could ever understand. Even though acapacitor appears to be a simple mechanism. The electron as the entireobservable universe, yet the electron as a closed loop of wire is thecomplex to the simple, but that is how axioms work. They allow themost complex to be contained into a simple term-- electron.

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Google's archives are top-heavy in hate-spew from search-engine-bombing. Only Drexel's Math Forum has done a excellent, simple andfair archiving of AP posts for the past 15 years as seen here: